Math, asked by sathawanemohan4, 7 months ago

if three no.s are added their sum is 2 .if 2 times the second no.s is subtracted from the sum of first and third no.is added to the sum of second and third no.we get 4 find the no, s using matrices​

Answers

Answered by sbarge230
1

Answer:

ANSWER

Let three numbers be x,y,z.

From given conditions, we have

x+y+z=2 .............(1)

x+z−2y=8

x−2y+z=8 ...........(2)

And

3x+y+z=4 .........(3)

Given all equation can be written in matrix form as,

1

1

3

1

−2

1

1

1

1

x

y

z

=

2

8

4

Consider, AX=B

On multiplying A

−1

both sides, we get

A

−1

.A.X=A

−1

.B

X=A

−1

.B .............(4)

Now,

A

−1

=

∣A∣

1

Adj(A)

∣A∣=

1

1

3

1

−2

1

1

1

1

∣A∣=6

Now, for Adj(A), we need minors and co-factors.

M

11

=−3,M

12

=−2,M

13

=7

M

21

=0,M

22

=−2,M

23

=−2

M

31

=3,M

32

=0,M

33

=−3

Therefore,

A

−1

=

6

1

−3

2

7

0

−2

2

3

0

−3

From equation (4),

X=

6

1

−3

2

7

0

−2

2

3

0

−3

2

8

4

x

y

z

=

1

−2

3

Hence, x=1,y=−2,z=3.

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